Specifically, if pi contains itself, that means "pi - pi/b^k" is a terminating fraction N in base b", where b is your choice of base (like base 10), and k is some positive integer. So
pi = N/(1-b^k) which is rational.
(And if you set k=0, you get that pi "contains itself" in the sense that pi from the 1st digit onward is of course pi)
You’re probably thinking of set theory but the file system is about storing information in a sequence and an offset. Seen that way, π can be stored with offset 0.
If it's normal then it contains all finite strings uniformly in its base-b expansions. Pi is not a finite string so it wouldn't have to contain itself uniformly. More specifically if it contains itself then it's a rational number, but we know that pi is not a rational number. Note that we don't know whether pi is a normal real number.